Conjoint Analysis

University of San Francisco

Matt Meister

Overview

Conjoint analysis - intro & concepts
- Product design concepts
Conjoint analysis - steps to perform
- Identify a set of relevant product attributes
- Define reasonable levels for those attributes
- Create product profiles
- Obtain consumer preferences for profiles
- Analyze the data for each respondent
- Simulate market outcomes

Conjoint Analysis Introduction

Good product design begins with understanding customers

A market-oriented organization focuses on identifying and satisfying the needs and wants of its customers
Conjoint analysis is a powerful analytical tool that can aid managers in understanding and quantifying these needs and wants

Product design concepts

A product can be considered as a bundle of attributes
- Attributes provide value to consumers
Each attribute can attain one or more levels
- Levels are specific values of attributes

Product design concepts: Example

A computer can be described as:

	Attribute	Level 1	Level 2	Level 3
1	Processor	2.4 GHz	3.2 GHz
2	RAM	8 GB	16 GB	32 GB
3	Storage	520 GB	1040 GB	2080 GB
4	Price	$400	$800	$1,200
5	Color	Grey	Silver	Black

Sample profiles:

2.4 GHz processor, 8 GB RAM, 520 GB hard drive, $400 price, black
2.4 GHz processor, 16 GB RAM, 520 GB hard drive, $800 price, grey
3.2 GHz processor, 8 GB RAM, 1040 GB, hard drive, $800 price, silver
3.2 GHz processor, 32 GB RAM, 1040 GB hard drive, $1,200 price, silver

How do we know what product people will like?

Need a reliable method to measure preferences

Two approaches:
- Stated preference -Directly ask customers how much they value attributes
- Revealed preference -Elicit customer preferences for whole products (profiles) -Infer value of attributes from responses

Advantages of revealed preference approach

Easier for respondents
Hard to answer questions like:
- “How much do you value a 4 hour battery life on your VR headset?”
More accurate
- Counters tendency to rate all attributes as (equally) important

Conjoint: Revealed preference via experiment

Attributes are considered jointly
- Subjects rate/rank/choose between product profiles
- Subjects forced to make trade-offs for attribute levels
- Trade-offs reveal true valuation
Limitations
- Attributes must be known in advance
- Hard to handle a large (>10) number of attributes

Stages in conjoint analysis

Identify a set of relevant product attributes
Define reasonable levels for those attributes
Create product profiles
Obtain consumer preferences for profiles
Analyze the data for each respondent
Simulate market outcomes

Stages 1 & 2: Attribute & level selection guidelines

Attributes in conjoint should be:

Clear and unambiguous
Actionable by the firm
The total number of attributes should be kept low
- 5-6 is the average, most studies fall between 4 and 8
Levels should span the realistic range of possible values
- E.g., include price levels close to min and max of market prices
- Use qualitative research and pretests to decide on attributes and levels

Stages 1 & 2 example: VR Headset

Standalone:
- Yes vs no
Cellular network access:
- Yes vs no
Price:
- $400 vs $800 vs $1,200
Battery life:
- 4 hours vs 8 hours vs 12 hours

How many possible profiles are there

2 attributes with 3 levels and 2 with 2 levels?

$3 \times 3 \times 2 \times 2$

$= 36$

Stage 3: Create product profiles

Data collection needs simplification (why?)

Shrink total set to only include possible/realistic products
- No impossible combinations
Unrealistic products can ruin our data

Stage 4: Obtain consumer preferences for profiles

Rating
- Consumers see a set of profiles, rate each
  - Positives?
    - People are used to rating things
    - Simple
    - Straightforward
  - Negatives?
    - Not a choice! (Not economically relevant necessarily)
    - Ratings are not necessarily comparable across products
Ranking
Choice

Stage 4: Obtain consumer preferences for profiles

Rating
Ranking
- People see all choices and rank them
  - Positives?
    - Simple
    - Straightforward
  - Negatives?
    - Still not a choice
    - What if things aren’t evenly spaced?
Choice

Stage 4: Obtain consumer preferences for profiles

Rating
Ranking
Choice
- People see options (usually 2+ at a time) and choose
  - Positives?
    - Real!
    - Potentially simple
  - Negatives?
    - Need a lot of trials

Stage 5: Data analysis

Typically, conducted at the individual level
Recovers a set of utility parameter estimates for each individual
Mode of analysis dependent on response format:
- Ratings data — linear regression (OLS)

Stage 5: Data analysis

Read in these responses to a conjoint survey for tablet computers

responses_DF <- read.csv("respondent_data.csv") # survey reponses ("Y" variables)
N <- nrow(responses_DF) # number of subjects
summary(responses_DF)

 respondent_id      profile_1   profile_2       profile_3      profile_4   
 Min.   :  1.00   Min.   :1   Min.   :1.000   Min.   :1.00   Min.   :1.00  
 1st Qu.: 39.50   1st Qu.:3   1st Qu.:4.000   1st Qu.:2.00   1st Qu.:1.00  
 Median : 73.00   Median :4   Median :5.000   Median :3.00   Median :2.00  
 Mean   : 74.17   Mean   :4   Mean   :4.675   Mean   :3.07   Mean   :2.14  
 3rd Qu.:113.75   3rd Qu.:5   3rd Qu.:6.000   3rd Qu.:4.00   3rd Qu.:3.00  
 Max.   :145.00   Max.   :7   Max.   :7.000   Max.   :7.00   Max.   :7.00  
   profile_5       profile_6      profile_7       profile_8       profile_9    
 Min.   :1.000   Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :1.000  
 1st Qu.:3.000   1st Qu.:2.25   1st Qu.:1.000   1st Qu.:2.000   1st Qu.:1.000  
 Median :4.000   Median :4.00   Median :2.000   Median :3.000   Median :1.000  
 Mean   :3.544   Mean   :3.86   Mean   :2.193   Mean   :2.974   Mean   :1.789  
 3rd Qu.:4.000   3rd Qu.:5.00   3rd Qu.:3.000   3rd Qu.:4.000   3rd Qu.:2.000  
 Max.   :7.000   Max.   :7.00   Max.   :7.000   Max.   :7.000   Max.   :6.000  
   profile_10      profile_11      profile_12      profile_13   
 Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
 1st Qu.:7.000   1st Qu.:2.000   1st Qu.:4.000   1st Qu.:2.000  
 Median :7.000   Median :3.000   Median :5.000   Median :3.000  
 Mean   :6.588   Mean   :3.114   Mean   :4.772   Mean   :3.202  
 3rd Qu.:7.000   3rd Qu.:4.000   3rd Qu.:6.000   3rd Qu.:4.000  
 Max.   :7.000   Max.   :6.000   Max.   :7.000   Max.   :7.000  
   profile_14      profile_15      profile_16      profile_17      profile_18  
 Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00  
 1st Qu.:1.000   1st Qu.:2.000   1st Qu.:2.000   1st Qu.:2.000   1st Qu.:2.00  
 Median :2.000   Median :3.000   Median :4.000   Median :3.000   Median :3.00  
 Mean   :2.351   Mean   :3.158   Mean   :3.693   Mean   :3.386   Mean   :3.14  
 3rd Qu.:3.000   3rd Qu.:4.000   3rd Qu.:5.000   3rd Qu.:4.000   3rd Qu.:4.00  
 Max.   :5.000   Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.00

Stage 5: Data analysis

For tablet computers, a relevant set of product attributes might be:

Screen size (inches)
Cellular network connectivity
Price
Battery life (hrs)
Operating system (OS)

Stage 5: Data analysis

For tablet computers, a relevant set of product attributes might be:

Attribute	1	2	3	4	5
Level	Screen (in)	Cell	Price ($)	Battery (hr)	OS
1	7	N	100	4	Android
2	10	Y	300	8	iOS
3			500	12	Windows

Stage 5: Data analysis

For tablet computers, a relevant set of product combinations might be:

Profile #	Screen (in)	Cell	Price ($)	Battery (hr)	OS
1	7	Y	300	12	iOS
2	7	Y	100	8	iOS
3	10	Y	500	12	Windows
4	7	Y	300	4	Windows
5	7	N	300	8	Android
6	10	N	300	12	iOS
7	7	N	500	12	Windows
8	10	N	300	8	Windows
9	7	N	500	4	iOS
10	10	Y	100	12	Android
11	10	Y	300	4	Android
12	7	N	100	12	Android
13	10	Y	500	8	iOS
14	10	N	500	4	Android
15	10	N	100	4	iOS
16	10	N	100	8	Windows
17	7	Y	500	8	Android
18	7	Y	100	4	Windows

Stage 5: Data analysis

design_DF <- read.csv("survey_design.csv") # survey design ("X" variables)
design_DF

   Screen Cell Price Battery      OS
1       7    Y   300      12 Windows
2       7    Y   100       8 Windows
3      10    Y   500      12 Android
4       7    Y   300       4 Android
5       7    N   300       8     iOS
6      10    N   300      12 Windows
7       7    N   500      12 Android
8      10    N   300       8 Android
9       7    N   500       4 Windows
10     10    Y   100      12     iOS
11     10    Y   300       4     iOS
12      7    N   100      12     iOS
13     10    Y   500       8 Windows
14     10    N   500       4     iOS
15     10    N   100       4 Windows
16     10    N   100       8 Android
17      7    Y   500       8     iOS
18      7    Y   100       4 Android

Stage 5: Data analysis

Let’s say we have a customer who responds to those profiles like this:

response <- c(3,4,4,2,4,4,3,4,1,7,4,6,2,3,4,6,4,5)

est_DF <- cbind(design_DF, response=response)

lm1 <- lm(response ~ factor(Screen) + factor(Cell) + factor(Price) + 
            factor(Battery) + factor(OS), 
          data=est_DF)

summary(lm1)


Call:
lm(formula = response ~ factor(Screen) + factor(Cell) + factor(Price) + 
    factor(Battery) + factor(OS), data = est_DF)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.58889 -0.18681 -0.01806  0.12778  0.57778 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         4.3472     0.3164  13.742 2.41e-07 ***
factor(Screen)10    0.6750     0.2093   3.225  0.01041 *  
factor(Cell)Y       0.0750     0.2093   0.358  0.72839    
factor(Price)300   -1.8333     0.2548  -7.195 5.11e-05 ***
factor(Price)500   -2.5000     0.2548  -9.812 4.19e-06 ***
factor(Battery)8    0.8333     0.2548   3.271  0.00967 ** 
factor(Battery)12   1.3333     0.2548   5.233  0.00054 ***
factor(OS)iOS       0.6667     0.2548   2.617  0.02797 *  
factor(OS)Windows  -1.0000     0.2548  -3.925  0.00349 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4413 on 9 degrees of freedom
Multiple R-squared:  0.9536,    Adjusted R-squared:  0.9124 
F-statistic: 23.12 on 8 and 9 DF,  p-value: 3.972e-05

Stage 5: Data analysis

Ratings Data

Intercept captures utility of “baseline” profile
- Baseline profile corresponds to all omitted attribute levels
Part-worths measure incremental utility relative to the baseline
- Part-worths of included attribute levels = regression coefficients
- Part-worths of omitted attribute levels = 0 by definition

Stage 5: Data analysis

Ratings Data

What is the baseline profile?
- The baseline profile is the profile associated with the omitted factor levels from the dummy variable coding. In this case, the baseline profile is a 7” screen, no cellular connectivity, $100 price, 4 hour battery life, and Android OS.
What is the expected utility (rating) for the baseline profile?
- The utility/rating for this profile is given by the intercept estimate.
- 4.3472
Interpret the coefficients from the regression
- Dummy variable coefficients represent in the incremental utility (rating), relative to the baseline profile
- e.g., the coefficient on factor(Screen)10 represents the incremental utility of changing from a 7” screen to a 10” screen

Step 5: Data analysis

Generate similar estimates for each individual represented in our supplemental data, responses_DF

How?

Create an empty list-of-lists to hold the regression results for each individual
- lm_res <- vector(mode = "list", length=nrow(responses_DF))
Loop over individuals. For each individual i:
- Create a dataframe that combines design_DF with the responses for individual i.
Estimate a linear model with individual i’s responses as the dependent variable, and the columns of design_DF as (factor) regressors
Store the linear model results to the i’th element of lm_res.
- To access or assign (top level) lists in a list-of-lists, we must use double bracket indexing, as in: lm_res[[i]]

Step 5: Data analysis

## estimate regression models, 1 per individual
# initialize an empty "list of lists" to hold lm() regression results
lm_res <- vector(mode="list", length=nrow(responses_DF))
# loop over subjects
for (i in 1:nrow(responses_DF)) {
  # get survey reponses for subject i (dropping respondent_id)
  response = as.numeric(responses_DF[i,2:ncol(responses_DF)])
  # create "estimation" dataframe, including i's reponses (Y) and the design variables (X)
  est_DF = cbind(design_DF, response=response)
  # run regression for subject i, store as lm_res[[i]]
  # note use of double bracket indexing [[ ]] syntax to access top-level lists
  lm_res[[i]] = lm(response ~ factor(Screen) + factor(Cell) + factor(Price) + 
                     factor(Battery) + factor(OS),
                   data=est_DF)
  }

Stage 6: Simulate market outcomes

Consider a hypothetical market
- Start with closest approximation to current competitive landscape
- Add 1st new product under consideration for introduction
Compute expected utility for each of the products, for each subject in the sample
Predict market shares (or units sold) for all products:
- Assume subjects choose product with the highest utility
- Product share = fraction of subjects who choose that product
Repeat steps above for remaining new product designs
- Introduce product concept with highest expected profit/market share

Stage 6

Conjoint allows us to evaluate “what if” scenarios
- How would a hypothetical “new” product would fare in competition with existing products?
In the context of our example
- How a new product by Toshiba will compete against the existing iPad
- Assume the existing “iPad” product corresponds to:
  - Screen = 10 (inches)
  - Cell = “Y” (has cell connectivity)
  - Price = 500 ($)
  - Battery = 8 (hrs)
  - OS = “iOS”

Stage 6

Assume (initially) that Toshiba is considering one potential product design, Toshiba_A

Screen = 7 (inches)
Cell = “N” (no cell connectivity)
Price = 300 ($)
Battery = 12 (hrs)
OS = “Android”
The cost to produce a tablet computer is:
- $(75 + 5\times(Screen==10) + 20\times(Cell==Y) + 5\times(Battery==8) + 15\times(Battery==12))$

Stage 6

Define Toshiba_A as the first product and the iPad as the second in a dataframe:

prods1 <- data.frame(Screen = c(7,10),
                     Cell = c("N","Y"),
                     Price = c(300,500),
                     Battery = c(12,8),
                     OS = c("Android","iOS"))

rownames(prods1) = c("Toshiba_A","iPad")
prods1

          Screen Cell Price Battery      OS
Toshiba_A      7    N   300      12 Android
iPad          10    Y   500       8     iOS

Stage 6

Use lm1 to predict a choice between the iPad and Toshiba_A

Hints:

Compute the utility (rating) that each consumer would derive from each alternative. You can use predict() for this task.
Predict choice as the product with the highest utility (rating). The which.max() function can be useful here

ratings = predict(lm1, newdata=prods1)
choice = which.max(ratings)
P = prods1[1,"Price"]
MC = (75 + 5*(prods1[1,"Screen"]==10) + 20*(prods1[1,"Cell"]=="Y") + 5*(prods1[1,"Battery"]==8) + 15*(prods1[1,"Battery"]==12))
profit = (choice==1)*(P-MC)

Stage 6

Discussion

Which product did the model predict we would choose?
- iPad
What is the cost of Toshiba_A?
- Toshiba_A costs $75 + 15 = \$90$

Stage 6

Predict choices for supplemental survey respones

Create a function called tablet_pft1 that takes as inputs:
- lm_res containing regression results for all subjects
- prods, a dataframe containing product definitions, as in the previous section
tablet_pft1 should return:
- profit - the profit for Toshiba’s product (product 1)
- cost - the cost of Toshiba’s product (product 1)
- choices - predicted product choices for each subject in responses_DF (a list)

Stage 6

Predict choices for supplemental survey respones

## function: tablet_pft1
# inputs:
# lm_res = list of lm() regression results
# prods_DF = dataframe of product definitions
# outputs:
# choices = predicted choice of each subject (list)
# cost = cost of product 1
# profit = profit of product 1
tablet_pft1 <- function(lm_res, prods_DF) {
  # initialize
  N = length(lm_res) # number subjects
  choices = rep(0,N)
  # loop over subjects: predict ratings/utilities, determine expected choices
  for (i in 1:N) {
    ratings = predict(lm_res[[i]], newdata=prods_DF)
    choices[i] = which.max(ratings)
    }
  # calculate demand, cost, profits for product 1 (1st row in prods_DF)
  Q = sum(choices==1)
  P = prods_DF[1,"Price"]
  MC = (75 + 5*(prods_DF[1,"Screen"]==10) + 20*(prods_DF[1,"Cell"]=="Y") + 
          5*(prods_DF[1,"Battery"]==8) + 15*(prods_DF[1,"Battery"]==12))
  pft = Q*(P-MC)
  # return values
  return(list(choices=choices, cost=MC, profit=pft))
  }

Stage 6

Use tablet_pft1 to report:

profits for Toshiba_A
demand (expected units sold) for Toshiba_A
the cost of Toshiba_A
Hints
- For each subject, compute the utility (rating) that each consumer would derive from each alternative
- For each subject, predict choice as the product with the highest utility (rating)

# call tablet_pft1 using prods1
prods1.results <- tablet_pft1(lm_res, prods1)
prods1.results$profit # profits

[1] 7350

sum(prods1.results$choices==1) # units sold

[1] 35

prods1.results$cost # marginal cost

[1] 90

Stage 6

Toshiba_B alternative product

Assume Toshiba is considering between releasing the Toshiba_A product and Toshiba_B
- Screen = 10 (inches)
- Cell = “N” (no cell connectivity)
- Price = 300 ($)
- Battery = 12 (hrs)
- OS = “Android”
Repeat the analysis above, assuming the iPad competes against Toshiba_B only

Stage 6

Toshiba_B alternative product

prods2 <- data.frame(Screen=c(10,10),
                    Cell=c("N","Y"),
                    Price=c(300,500),
                    Battery=c(12,8),
                    OS=c("Android","iOS"))
rownames(prods1) <- c("Toshiba_B","iPad")

Stage 6

Toshiba_B alternative product

prods2.results <- tablet_pft1(lm_res, prods2)
prods2.results$profit # profits

[1] 9635

sum(prods2.results$choices==1) # units sold

[1] 47

prods2.results$cost # marginal cost

[1] 95

Stage 6

Toshiba_B alternative product

Which product should Toshiba introduce?
- The profit from Toshiba_B is higher ($9635 vs $7350), so Toshiba should go with product B

Stage 6

Search over all Android OS alternative products

The trick here is first to enumerate all possible Android-based tablet designs. The expand.grid() function is useful for this purpose
After enumerating all possible Android-based tablet designs, loop over the designs and compute profits as before. Store the profit values in a list.
Find the element of the profit list with the highest profit. Use the index value for this profile to print the associated product attribute levels.

Stage 6

# create dataframe will all combinations of screen/cell/price/battery
allprods_DF <- expand.grid(unique(design_DF$Screen),
                           unique(design_DF$Cell),
                           unique(design_DF$Price),
                           unique(design_DF$Battery))
colnames(allprods_DF) <- c("Screen","Cell","Price","Battery")

Stage 6

Np <- nrow(allprods_DF) # number of products to test
# calculate profits for each candidate product, assuming iPad competition
pft <- rep(0,Np)
for (i in 1:Np) {
  prods = data.frame(Screen=c(allprods_DF[i,"Screen"],10),
                     Cell=c(as.character(allprods_DF[i,"Cell"]),"Y"),
                     Price=c(allprods_DF[i,"Price"],500),
                     Battery=c(allprods_DF[i,"Battery"],8),
                     OS=c("Android","iOS"))
  prods.results <- tablet_pft1(lm_res, prods)
  pft[i] <- prods.results$profit
}

Stage 6

# profit
max(pft)

[1] 15015

# change from Toshiba_B
max(pft)-prods2.results$profit

[1] 5380

100*(max(pft)-prods2.results$profit)/prods2.results$profit

[1] 55.83809

# profit-maximizing product
allprods_DF[which.max(pft),]

   Screen Cell Price Battery
10     10    Y   500      12

Guidelines

Do not use too many attributes (<= 6)
- More attributes increases the burden on consumers in at least two ways
  - Longer questionnaires
  - Makes each question harder to answer, because products become harder to evaluate
Focus on the attributes for which managerial decisions need to be made
Do not use subjective attributes or ambiguous level descriptions
Avoid infeasible combinations